Influences of heat release, blockage ratio and swirl on the recirculation zone behind a bluff body

ABSTRACT The recirculation zone created through vortex breakdown mechanisms in swirling flows plays a vital role for aerodynamic stabilization of turbulent flames in practical combustion systems. This zone interacts with the central recirculation zone (CRZ) of an upstream bluff body and this leads to a complex flow behavior that depends on the blockage ratio and swirl number. It has been previously observed that the vortex breakdown bubble (VBB) merges with the CRZ at large swirl number or blockage ratio. In this study, the influences of heat release on this flow structure and their physical mechanisms are explored through a series of large eddy simulations and experiments of bluff body stabilized premixed flames with swirling flows. Comparisons of simulation results with measurements are good. It is observed that in isothermal flows, as the swirl number or blockage ratio is increased, the vortex breakdown bubble moves upstream and its mean structure changes. The effect of heat release leads to considerable differences in the flow characteristics as the vortex breakdown bubble is pushed downstream due to dilatation. The critical swirl number, at which the VBB and CRZ merge, is observed to be higher in reacting flows for the same blockage ratio.


Introduction
There are various methods to stabilize turbulent flames with two of the most popular ones being the use of bluff bodies and swirl.The wake behind the bluff body creates a central recirculation zone (CRZ) consisting of a closed toroidal vortex.This flow structure emerges because of the transfer of momentum from the flow to the bluff body.The vortical structures emerging from the shear layer grow in time due to Kevin-Helmholtz instabilities (Vanierschot and Van den Bulck 2008).This translates into a high level of turbulence which enhances mixing and creates favorable conditions for the flame to stabilize.Many past studies on isothermal flows, for example by Chigier and Beer (1964); Ko and Chan (1979); Taylor and Whitelaw (1984), and reacting flows by Pan, Vangsness, and Ballal (1992); Fureby and Möller (1995); Massey, Langella, and Swaminathan (2019) investigated the characteristics of the CRZ in detail.Massey, Langella, and Swaminathan (2019) showed that there is a simple scaling relation for the length of this recirculation zone as a function of turbulence intensity at the bluff body base and the amount of heat release from the flame by considering various forces acting on the recirculation zone.This CRZ provides heat and radicals for flame stabilization.
Swirl in the flow adds further complexities by creating a vortex breakdown bubble (VBB) when this flow expands into a larger region (downstream of a bluff body).This is because the axial momentum is unable to overcome the adverse pressure gradient created by the expanding flow (Escudier 1988;Gupta, Lilley, Syred 1984;Lucca-Negro and O'Doherty 2001).It is generally accepted that a swirl number greater than 0.6 is required for the VBB to form (Gupta, Lilley, Syred 1984;Liang and Maxworthy 2005;Lucca-Negro and O'Doherty 2001).The swirl number can be defined as the ratio of azimuthal to axial momentum fluxes in the axial direction, written as (Beer and Chigier 1972): In Equation (1), R p is the inner radius of inlet pipe and u x and u θ are the axial and azimuthal components of the velocity respectively.Experimental studies use alternative definitions based on the geometric characteristics of the swirler.Therefore, care must be taken when comparing the swirl numbers from different studies, as the geometric swirl number can be significantly different to S from the above equation (Litvinov et al. 2021).
A more complex swirling flow pattern is observed in the presence of a bluff body which consists of a CRZ and a VBB further downstream.This swirling CRZ has a more complicated structure compared to non-swirling flows with more than one vortices appearing and is highly dependent on the swirl number.This happens as the centrifugal forces are balanced by the swirl-induced radial pressure gradient (Percin, Vanierschot, Oudheusden 2017;Vanierschot and Van den Bulck 2008).A cross section of a typical flow at low swirl numbers is shown schematically in Figure 1a, while Figure 1b shows the flow at higher swirl numbers.In Figure 1a, vortex 1 forms the VBB and vortices 2 and 3 form the CRZ.
The VBB created because of low pressure in the wake can be observed at low swirl numbers even in the presence of a simple rod aligned with the flow (Huang and Tsai 2001;Sarpkaya 1974;Sheen, Chen, Jeng 1996).The flow structure is similar to that shown in Figure 1a.However, the VBB moves upstream as the swirl number is increased and it eventually merges with CRZ forming a single large CRZ as shown schematically in Figure 1b.This was observed by Escudier and Keller (1985), Sheen, Chen, and Jeng (1996), Vanierschot and Van den Bulck (2008) and Sheen, Chen, and Jeng (1996) also reported that the structure of this enlarged CRZ did not change for Reynolds numbers above 500.
A few studies cited below investigated the effect of blockage ratio, BR, on these structures in swirling flows.The BR is defined as the ratio of the cross section area of the center body to that of the inlet pipe: where D 0 and D p are the diameters of the bluff body and inlet pipe respectively as marked in Figure 1.Generally, increasing BR has a similar effect to increasing the swirl number (Huang and Tsai 2001;Mukherjee et al. 2021).The flow had no clear structure and was highly unstable when the VBB merged with the wake (Huang and Tsai 2001).
Study on heat release effects in bluff body swirling flows is scarce.Although a number of studies have explored reacting bluff body flows with swirl, most of them focused on flame shape (Balachandran 2005;Lovett and Mick 1995;Worth and Dawson 2013;Zhang et al. 2019) or the interrogation window was too small to fully capture the relevant flow features (Dupuy et al. 2020;Sweeney et al. 2012).Schneider, Dreizler, and Janicka (2005) observed a single CRZ similar to that shown in Figure 1b for both reacting and non-reacting conditions but the swirl number was quite high, S � 0:8 and the blockage ratio was low, BR � 0:25.Chterev et al. (2014) studied the flame shape and flow patterns in annular swirling flows and observed that (1) the jet angle with respect to the flow axis increased and (2) additional stagnation points appeared along the centreline in the wake region of reacting flows.However, they did not explore the changes in VBB as the values of S and BR are changed.
The interaction between the CRZ and VBB influences the stability of the flame root which has not been explored in detail in previous studies.Hence, the main objective of this paper is to investigate the effects of heat release on the CRZ structure and its interaction with VBB in swirling flows with bluff bodies.A range of swirl number and BR, detailed later, are considered for Large Eddy Simulation (LES) and experimental measurements.
The paper is organized as follows.In section 2 the experimental setup is described along with a brief description on the experimental techniques used.The LES model and computational setup are discussed in section 3. The results are presented in section 4 and conclusions are summarized in the final section.

Burner details
The schematic of the bluff body stabilized burner has been described in detail by Ajetunmobi, Talibi, and Balachandran (2019) and only a brief description highlighting the essential features is included here.The plenum has an internal diameter of 100 mm and a total length of 300 mm, including the convergent and divergent sections.The duct leading from the plenum has an internal diameter D p 35 mm and a length of 400 mm.Two conical bluff bodies, with diameters D 0 of 25 mm and 30 mm, giving blockage ratios of BR ¼ 51% and 73% respectively, are used in this study.A 100 mm cubical enclosure is placed on the burner plate, which prevents ambient air entrainment and allows optical access for diagnostics.The burnt gases exit through a 79:5 mm circular hole on a 8 mm thick metal plate exit cover that formed an integral part of the combustor.An axial swirler is placed at 42 mm upstream of the bluff body base.A swirler with 8 flat vanes positioned at 45 � with respect to the flow is used for the experiments.The swirl numbers, calculated using Equation (1), are measured at the dump plane and depend on the bluff body, as the blockage ratio has a significant effect on the swirl number.For the reacting cases, a premixed ethylene-air mixture with an equivalence ratio of ϕ ¼ 0:52 is used and this mixture is at room temperature and atmospheric pressure when entering at the bottom of the burner, see Figure 2.For all experiments, the mean bulk axial velocity at the bluff body base, u 0 , is fixed at 10 m/s.

PIV technique
Two-dimensional PIV (Particle Image Velocimetry) is used to investigate mean flow field structures experimentally.A 5 watt, 532 nm dual-pulsed Nd:YAG laser (Quantel Evergreen) is used in conjunction with sheet-making optics, to generate a collimated laser sheet with 1 mm thickness.A CCD camera with 4 million pixels (TSI POWERVIEW), mounted with a 45 mm macro lens (aperture f =8), is placed orthogonally to capture the Mie-scattered images at 3 Hz repetition rate (same as Nd:YAG laser).1A polarizer and filter (532 � 10 nm) are used to prevent unwanted light and reflections.The measured field of view (FOV) is approximately 100 � 80 mm with a spatial resolution of � 45 μm.A TSI particle generator (3410 L) is used to seed the air flow with TiO2 particles ( � 1 μm diameter, density 4:26 g/cc).Part of the primary air is redirected through the particle generator to create a seeding stream, before being recombined upstream of the plenum.

Data processing and error analysis
Five hundred image pairs are captured for each test condition.The time between two laser pulses δt is set to 18 μs, to ensure that the maximum in-plane pixel displacement is within one-fourth of the integration area (IA).The scale factor for the images in the present study is 0:05 mm per pixel, resulting in an IA of 1:6 mm 2 , corresponding to a spatial resolution of 0:8 mm between two neighboring vectors in both longitudinal and traverse directions.The images are background noise corrected, and spurious velocity vectors ( < 2%) are removed using a universal outlier detection method (Nogueira, Lecuona, Rodríguez 1997).The correlation peak is calculated using a three-point Gaussian estimator, giving a sub-pixel accuracy of 0:1 pixels (Raffel et al. 2007), and corresponding to an accuracy of 0:025u 0 for both instantaneous axial and radial velocities for all the bulk velocities tested.Preliminary analysis is done to determine that the sample image number N of 500 is sufficient for the convergence of mean velocities and corresponding standard deviations (σ).Random errors in the mean velocity estimates are given by u rms = ffi ffi ffi ffi N p (Chterev et al. 2014), where u rms is the root mean square velocity.Using N ¼ 500, the mean velocity uncertainties is approximately 9% of the largest u rms measured.Also, the mean and rms velocities calculated by progressively increasing the sample image numbers showed that these statistics remain the same when the image number is beyond 150 suggesting that 500 samples are adequate for the conditions investigated.

Large eddy simulation
The six cases simulated are listed in Table 1 along with the experimental cases.Combinations of three swirlers and two bluff bodies are used.The three swirlers, S30, S45 and S60, used in the simulations have vanes of 30 � , 45 � and 60 � degrees respectively and the diameter D 0 of the two bluff bodies, BB25 and BB30, is 25 mm and 30 mm.Two of those cases, marked in Table 1 are validated through experiments.A prefix 'NR' or 'R' is added in front of the case ID in the discussion below to denote non-reacting or reacting cases respectively.The computational model is an accurate representation of the experimental  setup including a 2 mm radial gap between the central support rod and swirler hub in S45-BB25P.Experiments show that this gap is required for providing purge air to avoid the flame stabilizing on the swirler in the lower BR cases.The effects of this purge air on the CRZ and its interactions with VBB are also investigated using LES by considering an additional case S45-BB25 without the gap, which in effect increases the swirl number.Details on the equations solved and the closure models used are discussed next.
The compressible Favre-filtered transport equations for mass and momentum are solved, and these equations are: The fluid density is ρ, u is the i th velocity component, p is the pressure and τ ij is the molecular shear stress.The last term in Equation ( 4) is the residual stress tensor, which is modeled using the Boussinesq hypothesis (Smagorinsky 1963) where Δ is the LES filter width, S ij is the symmetric strain rate tensor and the model parameter, C S , is obtained using a dynamic procedure (Germano et al. 1991;Lilly 1992).
For reacting flows, four additional filtered transport equations are solved.These are for the total enthalpy e h (the sum of sensible and chemical enthalpies), the reaction progress variable e c, its sub-grid variance σ 2 c; sgs , and the mixture fraction e �.The definition of the progress variable is carefully chosen so that it takes values equal to zero and unity in reactant and fully burnt mixtures respectively with a monotonic increase from reactants to products.It is defined using , where the subscript 'b' denotes burnt conditions.The mixture fraction is defined using the definition proposed by Bilger (1988) and it is used as a marker for reactant stream in premixed systems.This helps to treat the mixing of burnt products with ambient air open flames.These transport equations are written in the compact form, with φ ¼ f h ; c ; σ 2 c;sgs ; �g, as The effective diffusivity is modeled as , where D φ is the molecular diffusivity for φ.This is taken to be the thermal diffusivity, α, for enthalpy.For the other scalars, D φ ;ν=Sc, where Sc ¼ 0:7 is the molecular Schmidt number.The turbulent Prandtl number Pr T ¼ 0:4 is used for σ ϕ in the enthalpy equation, whereas for the other scalar equations, the parameter is σ φ ;Sc T .The turbulent Prandtl and Schmidt numbers are equal to 0:4 following previous studies (Chen, Ruan, Swaminathan 2017;Pitsch and Steiner 2000).
The density is obtained from the equation of state ρ ¼ p e M=< 0 e T, where e M and < 0 are the molecular mass and the universal gass constant respectively.The filtered temperature e T is obtained from the enthalpy transport equation as e where f Δh 0 f and e c p are the enthalpy of formation and specific heat capacity respectively, and T 0 ¼ 298:15 K.
The sources S þ φ and sinks S À φ in Equation ( 6) are respectively written as The sub-grid scalar dissipation rate (SDR) term e χ c;sgs requires closure in the transport equation for σ 2 c;sgs .The algebraic expression proposed by Dunstan et al. (2013) and employed in previous studies (Chen, Ruan, Swaminathan 2017;Langella and Swaminathan 2016;Massey, Langella, Swaminathan 2018), is used to model e χ c;sgs , since it includes the effects of chemical reactions, thermal expansion and the multi-scale turbulence-combustion interactions.
The other terms requiring closures are the filtered reaction rate terms in Equation ( 7).A presumed probability density function (PDF) approach is used to obtain these terms.The reaction rate _ ω c is calculated using where _ ω c ζ ð Þ and ρ ζ ð Þ are the flamelet reaction rate and mixture density which are obtained from one-dimensional unstrained premixed flame calculations using Cantera code with the USC chemical mechanism for ethylene-air combustion (Wang and Laskin 1998).The scaled flamelet reaction rate is determined as The density-weighted PDF is obtained using a distribution e PðζÞ ¼ P β ðζ;e c; σ 2 c;sgs Þ to construct a look-up table for the filtered reaction rate.The thermochemical parameters, e M, f Δh 0 f and e c p , are stored in the look-up table following Ruan, Swaminathan, and Darbyshire (2014).As noted eariler, the transport equation for e � is included to track the dilution of burnt products with air as this influences the local thermochemical parameters.The source term c _ ω c is determined in a similar form as Equation ( 9) following previous studies (Chen, Ruan, Swaminathan 2017; Langella and Swaminathan 2016).

Computational setup
Six unstructured meshes with tetrahedral cells are used.The number of mesh cells range between 2.5 and 2.9 million since the geometrical features of the bluff bodies and swirlers change.However to maintain consistency, the cell distribution and densities in the entire domain are kept to be almost the same for all cases.The computational domain, shown in Figure 2 for case S45-BB30, includes the swirler, burner and an extended cylindrical domain of 500 mm long and 700 mm diameter downstream of the burner outlet.This extended domain is for two reasons; (i) to specify unambiguous boundary conditions at the outlet and (ii) to capture the VBB as it is observed to extend beyond the combustor length in experiments.A grid sensitivity study is also tested using case NR-S45-BB30 employing three meshes with up to 6.2 million cells.It is observed that there are no differences in the physical features of the flow and therefore the coarsest mesh (2.5 million cells) was used to save the computational cost.The simulations are performed using OpenFOAM 7 with the PIMPLE algorithm for pressure-velocity coupling.Second-order numerical schemes are used for spatial derivatives and a first-order implicit Euler time marching scheme is employed to ensure numerical stability.The timestep size, ranging from 6 to 20 μs, is employed to ensure that the maximum CFL number in the domain does not exceed 0.4.The timestep is reduced by up to 45% for reacting flow calculations.
All the walls are specified to be adiabatic and no-slip with wall functions.For ethylene-air inlet boundary, a constant mean velocity with random noise has been prescribed at the inlet with an inlet turbulence intensity of 5%.A non-reflective boundary condition for pressure and a zero-gradient condition for the other scalar variables are prescribed at the outlet.The simulations are performed using the ARCHER2 UK national high performance computing facility.
For each case, the statistics are obtained using samples collected for at least 10 flowthrough times based on u 0 and the entire computational domain length L in Figure 2, after a transient period of 3 flow-through times.This substantial computational period is required to obtain converged time-averaged statistics.

Validation & flow structure
The swirl number S for each case, obtained using Equation (1) at the bluff body base, is shown in Table 1.It is evident that a specific swirler yields a higher swirl number for a smaller BR, which is consistent with the experimental observation of Litvinov et al. (2021) showing a decrease in S as the exit area of a contracting nozzle is reduced.
As noted in Table 1, measurements are taken for the two isothermal cases NR-S45-BB25P and NR-S45-BB30.The comparison of the mean axial velocity contours and streamlines between LES and experiments is shown in Figure 3.The measurements are shown on the left half with LES results on the right.The white lines correspond to zero axial velocity.It can be seen that for case NR-S45-BB25P in Figures 3a and 3b, the CRZ and VBB are separated.The CRZ consists of two axisymmetric counter rotating toroidal vortices, as seen in the streamline plot in Figure 3a, with a positive axial velocity at the centreline, as seen in Figure 3b.The absence of a stagnation point along the central line in the CRZ region is because the inner vortex has enough momentum to overcome the reverse flow (Sheen, Chen, Jeng 1996).In the VBB in case NR-S45-BB25P, another vortex can be seen at 60 < x < 140 mm in Figure 3a and some smaller ones around a thin region of negative velocity at 30 < x < 60 mm.The negative axial velocity magnitude in the VBB is small compared to that in the wake region as seen in Figure 3b.A very similar structure can be observed for NR-S45-BB30 shown in Figures 3c and 3d.The flow features in the CRZ are identical to those in case NR-S45-BB25P, while the VBB is observed to be larger.This is because the higher swirl number in case NR-S45-BB25P produces a more compact VBB.
The comparisons between experiments and LES seen in Figure 3 for case NR-S45-BB25P are very good.The axial distance of the VBB formation is captured well in the LES, but with some small differences in the initial width of the VBB.This is also confirmed when the radial profiles of the mean and rms axial and radial velocities are analyzed at different streamwise locations, as shown in Figures 4 and 5 for cases NR-S45-BB25P and NR-S45-BB30 respectively.A good agreement is observed for the mean velocities for case NR-S45-BB25P in Figure 4.The locations of the shear layers of the incoming reactant jet, as indicated by the steep velocity gradients, and the peak values of the axial and radial velocities compare well against the measured data for the region x=D 0 � 1:5.At x=D 0 ¼ 2, the location of the jet is closer to the centreline in the LES since the upstream part of the VBB is narrower compared to the measurements, as seen in Figure 3b.The radial locations of the peaks in the rms values also match the measurements which shows that the location of the shear layers are correctly predicted.An excellent agreement is also observed for case NR-S45-BB30 in Figure 5.The mean axial and radial velocities agree well with the experiments at all locations.The rms values are also well predicted apart from the distance x=D 0 ¼ 0:1 where the rms values are significantly lower.

Effects of swirl and blockage ratio on non-reacting flows
Before discussing the effects of swirl and BR on the structures of CRZ and VBB in isothermal flows, it is instructive to understand the effect of purge flow on these structures.As noted earlier, the purge flow is required in the experiments of S45-BB25 case to avoid the flame stabilizing on the swirler.In the first attempt of the LES, the 2 mm gap provided for the purge air in BB25 cases was not included in the computational geometry since the experiments were conducted after the simulations were completed.To keep the computational geometry close to the experimental case, a new case listed as S45-BB25P in Table 1 is created with the purge-air gap and the comparison of computed and measured results is very good as discussed in the previous section.This case is compared with S45-BB25 to understand the effect of purge air on the CRZ and VBB structure.The time-averaged axial velocity and streamlines are shown in Figure 6a for case NR-S45-BB25, which is compared with the LES results shown in Figure 3a and 3b for NR-S45-BB25P case.It is clear that the flow structure behind the bluff body is changed dramatically and the merged CRZ and VBB can be seen in Figure 6a, which is because the swirl number at the bluff body base increases by about 32% when there is no purge air gap.This change in the flow structure with the swirl number is consistent with previous studies and the effects of S and BR are discussed next using case NR-S45-BB25 as the baseline case, since the other five cases do not have the purge air gap.
Figure 6 shows that the VBB moves downstream when the swirl number is reduced to 0.32 in case NR-S30-BB25, shown in Figure 6b, compared to case NR-S45-BB25P, shown in Figures 3a and 3b, and this is consistent with several past isothermal flow studies (Escudier and Keller 1985;Sheen, Chen, Jeng 1996;Vanierschot and Van den Bulck 2008).In this particular case, the distance of the upstream stagnation point of the VBB to the bluff body base has almost doubled from 1:4D 0 in case NR-S45-BB25P to 2:6D 0 in case NR-S30-BB25.In addition, the VBB becomes wider because most of the VBB is located in the unconfined region downstream of the combustion chamber exit.However, the CRZ structure is the same with a small 10% reduction in the length of CRZ between these two cases.
On the other hand, when the swirl number is increased to 0.58 and 0.8 in cases NR-S45-BB25 and NR-S60-BB25, shown in Figures 6a and 6c respectively, the VBB is attached to the CRZ region.The inner vortex and the positive velocity along the centreline near the bluff body base almost disappear in case NR-S45-BB25 where a small region of positive velocity can be seen close to the bluff body and completely vanish in case NR-S60-BB25 where the mean axial velocity is negative in the entire CRZ.Furthermore, the CRZ appears to widen downstream in the higher swirl case, as observed in Figure 6c, which is because of the flow expansion in the radial direction allowing a larger CRZ and a smaller side recirculation zone, as observed by Sheen, Chen, and Jeng (1996).To summarize, increasing S does not change the structure of the CRZ in the range of swirl numbers and blockage ratios investigated, but leads to changes in the VBB structure.At high swirl numbers, the CRZ and VBB merge and the structure changes significantly.
The effect of blockage ratio can be understood by comparing case NR-S45-BB30 with case NR-S30-BB25 and case NR-S60-BB30 with case NR-S45-BB25P as these pairs have similar swirl numbers but a different BR as listed in Table 1.It is observed that the axial distance where the VBB forms is reduced by approximately 50% when the BR is increased from 0:51 to 0:73 for S � 0:3.This can be seen by comparing Figures 3c and 3d with Figure 6b.This is similar to the observations of Huang and Tsai (2001), who noted that increasing the blockage ratio moves the VBB upstream in swirling flows with disc shaped  1 bluff bodies.The length of the CRZ for case NR-S45-BB30 is 0:67D 0 and it is 0:88D 0 for case NR-S30-BB25, whereas the minimum axial velocity in the CRZ remains roughly the same (0:25u 0 ).Cases NR-S45-BB25P and NR-S60-BB30 have also almost the same swirl number but different BR values of 0:51 and 0:73 respectively and the same pattern can be observed.The VBB moves upstream when the BR value is increased by comparing the results shown in Figures 3a, 3b and 6d.Although the VBB has merged with the outer vortex of the CRZ in case NR-S60-BB30, the predominant structure of the CRZ having an inner vortex near the bluff body base has remained the same.In essence, increasing the blockage ratio moves the VBB closer to the CRZ without changing their structures.
The observations based on the mean fields imply the existence of a critical swirl number S c where the VBB attaches to the CRZ.This critical number is a function of the blockage ratio.At low swirl numbers the VBB and CRZ are separate, as seen in Figure 6b for case NR-S30-BB25, where the VBB is more than 1:5D downstream of the CRZ.As the swirl number increases and the distance between the VBB and CRZ decreases, there is some intermittent merging of the VBB and CRZ and the mean characteristics of the VBB start changing with smaller vortices appearing in its upstream part near the centreline.This is visible in cases NR-S45-BB25P and NR-S45-BB30 in Figures 3a and 3c respectively.When the swirl number exceeds S c , the outer vortex of the CRZ merge with the VBB forming a single recirculation zone which can be seen in case NR-S60-BB30.When the swirl number is further increased, the inner vortex is completely suppressed leaving two large vortices, as seen in case NR-S60-BB25.

Instantaneous CRZ structure
An interesting pattern can be observed when the instantaneous streamlines are studied in Figures 7 and 8.The streamlines at two randomly chosen times 200 ms apart are shown for cases NR-S45-BB25P, NR-S45-BB30, NR-S45-BB25 and NR-S60-BB30.The swirl number is smaller and higher than S c in the former two and latter two cases respectively.The features of the CRZ can be observed distinctly in both snapshots of NR-S45-BB25P and NR-S45-BB30 cases where the CRZ and VBB are not merged as depicted in Figure 7.The inner vortex in the CRZ that penetrates the outer one, creating a region of positive axial velocity along the centreline is visible in all snapshots and the size also remains similar.On the other hand, the instantaneous structure of the VBB is different from the mean structure, as seen in the streamline patterns, because the complex flow structures change significantly over time.In those two cases where the VBB is close to the CRZ, some intermittent merging occurs.
In cases NR-S45-B25 and NR-S60-BB30, with S > S c , the behavior observed in the VBB for the non-merged cases extends to the entire CRZ.While for case NR-S60-BB30 the CRZ is still distinguishable in Figures 8a to 8d, the intermittent merging and separation changes its instantaneous structure more significantly.For case NR-S45-BB25, in which the mean characteristics are completely different, the variations in the shape and size of the CRZ are a lot more significant with different size of vortices appearing without a fixed location.There is also a much bigger change in size over time.This behavior in cases NR-S45-BB25, NR-S60-BB25 and NR-S60-BB30 where the CRZ and VBB are merged, has also been observed by Huang and Tsai (2001).

Effects of heat release
Reacting flows are considered hereafter to understand the effect of heat release on the CRZ and the VBB structures.The reacting flow LES is validated first before discussing these results.Figure 9 compares the measured and computed mean axial velocity contours and streamlines for case R-S45-BB25P.The white lines correspond to zero axial velocity.Four major differences between the non-reacting and reacting cases can be observed by comparing Figures 3a, 3b and 9: (i) the upstream stagnation point of the VBB has moved from 1:4D 0 (35 mm) to 2D 0 (50 mm), (ii) the smaller vortices on the upstream end of the VBB have disappeared and there is only one large vortex, (iii) the CRZ has become longer, and (iv) the inner vortex is not penetrating the outer vortex in the CRZ creating two stagnation points along the centreline, as seen in Figure 9, which implies a flow structure different to that observed by Sheen, Chen, and Jeng (1996) in non-reacting flows, where the penetration does not necessarily occur when a VBB is formed.
These four major differences between the isothermal and reacting flows are observed in both LES and experiment.Furthermore, the comparison of LES and experimental results shown in Figure 9 for case R-S45-BB25P is very good.The sizes of the CRZ and the triangular region of positive velocity above the bluff body are well captured in the LES.The VBB though is not visible in the experiment because it is located outside the PIV window.2 Figure 10 compares the measured and computed mean and rms velocities and it is clear that the comparison is very good for mean velocities.The second order statistics compare satisfactorily.Although one may like to improve this comparison, the objective here is to understand the effect of heat release on the flow structure and the interaction between the CRZ and VBB.
In non-swirling bluff body flames under lean conditions, dilatation increases the size of the CRZ as the hot gases expand in the CRZ (Massey, Langella, Swaminathan 2019;Pan, Vangsness, Ballal 1992).In swirling flows, this implies that the VBB is pushed downstream from the bluff body base, which can be understood further by examining the mean static gauge pressure field in the combustor as seen in Figure 11.The mean gauge pressure along the centreline is shown in Figure 11a, while its spatial variation in non-reacting and reacting flows is shown in 11b.The gauge pressure is defined as ð < p s > À p amb Þ=ðρ u u 2 0 Þ where < p s > is the time-averaged static pressure, p amb is the ambient pressure and ρ u is the density of the unburnt mixture.It is apparent that the pressure in the CRZ of the non-reacting case is lower which pulls the VBB upstream.In addition, while the swirl number at the bluff body base remains the same in nonreacting and reacting cases, the axial and azimuthal momentum fluxes can change downstream due to dilatation and heat release, which affects the local swirl number.If the swirl number at the bluff body base is close to S c , small changes in S can lead to changes in the structure of the flow.On the other hand, if S is significantly lower than S c , the VBB will simply move further downstream.

Flame shapes in LES
The time-averaged flame shapes are shown in Figure 12.In the four cases with the 25 mm bluff body, the increase of swirl has three main effects on the flame: (i) the flame length is reduced, (ii) the width of the flame brush is increased as the reaction rate is distributed over a larger area and (iii) the flame angle with respect to the flow axis increases at higher swirl numbers.All of the above three points can be seen clearly by comparing Figures 12d, 12c and 12e as these cases have the same BR but different S as listed in Table 1.It is also worth noting that the reaction rate on the outer flame appears to become stronger as the swirl is increased and this is observed by comparing Figures 12a & 12 f, and 12d, 12c & 12e.Due to the highly unsteady VBB, ambient air can be entrained into the combustor from the sides of the enclosure and in low swirl cases this entrained air can easily reach the side recirculation zone near the bluff body base making the outer flame weaker.When the swirl is high, which yields a large flame angle as noted above, the entrained air is unable to reach the corner recirculation zone leading to a stronger outer flame.However, the reaction rate in the outer flame can be overestimated if the walls are treated as adiabatic as in many past studies (Armitage et al. 2006;Han and Morgans 2015;Ruan et al. 2016).There is no OH-PLIF data to compare with LES, but the flames observed by Balachandran (2005) using a similar burner and flow conditions appear to be close to those shown in Figure 12.

Effects of swirl and blockage ratio under reacting conditions
Figure 13 shows the mean axial velocity and streamlines for the various reacting cases considered.The CRZ structure is almost the same in all cases except for cases R-S60-BB25 and R-S60-BB30 shown in Figures 13c and 13e respectively.This allows a comparison in terms of how the swirl number and blockage ratio affect the characteristic lengths of the CRZ.This is shown in Figure 14a which shows the mean axial velocity along the centreline.Three lengths L A , L B and L C can be defined from the bluff body base to the locations where the axial velocity is zero.The length of the triangular region downstream of the bluff body is marked as L A where the velocity is positive and the streamwise axial velocity gradient is    negative.The CRZ length is marked using L B where the same gradient is positive and L C is the distance to the upstream stagnation point of the VBB.These three lengths are shown schematically in Figure 14c and their variation with S is shown in 14b.The upstream shift of VBB with increasing S and BR is signified by the variation of L C shown in Figure 14b, which is similar to the shift in non-reacting flows.The length L A remains mostly unaffected by S and BR when the VBB has not merged with the CRZ.A decrease is observed for S ¼ 0:8 where the VBB has merged with the CRZ.A weak relationship between S and L B is also apparent.For S ¼ 0:32 and S ¼ 0:44 the length is virtually the same and increased by about 14% when S is increased to 0.58.For the highest swirl case, L B increases significantly because the VBB has merged with the CRZ.On the other hand, a bigger change is observed when BR is increased.For BR ¼ 0:71, L B is reduced by 27% and L C is also reduced significantly as expected.
A few other interesting features can be observed by comparing Figures 9 and 13.The first one relates to cases R-S45-BB25 and R-S60-BB30, shown in Figures 13a and 13e respectively, where the VBB is close to the CRZ.The streamlines suggest that only a single toroidal vortex exists in the VBB.This implies that the mean VBB structure does not change as it moves closer to the CRZ as it did in the non-reacting flow.If the CRZ and VBB are close enough though, they can still merge intermittently as also observed for non-reacting flows.Under these conditions, the entire CRZ still becomes unstable when they fully merge.
For case R-S60-BB25 in Figure 13c, where the VBB has merged with the CRZ, the inner vortex is still apparent.This contradicts previous experiments by Schneider, Dreizler, and Janicka (2005) and Dupuy et al. (2020) where a region of positive velocity in the CRZ at similar swirl numbers is not seen.The blockage ratio used in those studies was much smaller (BR ¼ 0:25) and the shape of the bluff body is also different which suggests that this region exists due to the geometry of the central body.The sensitivity of the inner CRZ vortex to the geometry of the bluff body can also be confirmed in case R-S60-BB30 in Figure 13e.This is the only reacting case where the inner vortex has penetrated the outer vortex making the CRZ to widen in the downstream part as shown in Figure 13e.This implies that as the blockage ratio is increased, the strength of the inner vortex increases.A map of the cases studied in terms of swirl number and blockage ratio is shown in Figure 15.The Figure suggests that the critical number increases from 0:44 < S c < 0:58 in non-reacting flows to 0:58 < S c < 0:8 in reacting flows at BR ¼ 0:51.When the blockage ratio increases to 0:73, the critical swirl number is estimated to be reduced to 0:3 < S c < 0:42 for non-reacting flows.No merging was observed for the swirl numbers studied at high blockage ratio in reacting flows.This suggests that S c is higher in reacting flows under the equivalence ratio studied.

Conclusion
In this study six swirling flows with a range of swirl numbers and blockage ratios are simulated using LES under non-reacting and reacting conditions.Two non-reacting and one reacting case are also studied experimentally using PIV for validating LES results and the agreement is observed to be very good.
The flow behavior under non-reacting conditions is consistent with previous studies.As the swirl number is increased, the VBB moves upstream until it attaches to the CRZ behind the bluff body.This happens when the swirl number exceeds a critical value S c at which the VBB and CRZ merge.The VBB tends to be more unsteady than the CRZ and the entire CRZ becomes unstable once they merge.In addition, as the swirl number increases and approaches S c , the VBB can momentarily merge with the CRZ due to its oscillations.This can alter the mean characteristics of the VBB with small vortices appearing in a thin region upstream of the large vortex.Increasing the blockage ratio leads to merging of these structures at a lower S, suggesting a decrease in S c .
In reacting cases, heat release and dilatation leads to the displacement of the VBB downstream in cases where the swirl number is below S c .The inner vortex in the CRZ is also weakened and becomes unable to penetrate the outer vortex as it did in isothermal flows in all cases in which the VBB and CRZ are separated apart from case R-S60-BB30.When the swirl number is close to the critical value, changes in the flow structure can be observed implying that S c increases under the reacting conditions studied.Furthermore, the CRZ length in reacting flows increases compared to the isothermal flows because of heat release effects as noted by Massey, Langella, and Swaminathan (2019).It is also observed that this length is either unaffected or increases slightly with increasing S.
There are still many unanswered questions.The first is how turbulence intensity affects the length of the CRZ.The second is to quantify and develop a relationship between the critical swirl number and the blockage ratio for non-reacting and reacting flows.A single equivalence ratio is used for all cases in this study.At higher equivalence ratios, it has been found that the radial pressure forces compensate for the dilatation and cause the CRZ to shrink compared to the isothermal cases in non-swirling reacting flows (Massey, Langella, Swaminathan 2019).It will therefore be interesting to examine how the VBB behaves at different equivalence ratios.All of these will be explored in future studies.

Figure 1 .
Figure 1.Flow patterns behind the bluff body in swirling flows for (a) low swirl numbers and (b) high swirl numbers.

Figure 2 .
Figure 2. Typical numerical grid used for LES is shown in the mid-plane of the computational domain.

Figure 3 .
Figure 3. Comparisons of measured and computed streamlines and mean axial velocity for case NR-S45-BB25P shown in (a) and (b) respectively, and case NR-S45-BB30 in (c) and (d) respectively.The white lines are for zero axial velocity.Dimensions are in mm.

Figure 4 .
Figure 4. Comparison of measured and computed mean and rms velocity profiles at six different axial positions for isothermal flow of case S45-BB25P.

Figure 5 .
Figure 5.Comparison of measured and computed mean and rms velocity profiles at six different axial positions for isothermal flow of case S45-BB30.

Figure 9 .
Figure 9.Comparison of measured and computed mean axial velocities and streamlines for case R-S45-BB25P.The white lines are for zero axial velocity.

Figure 10 .
Figure 10.Comparison of measured and computed mean and rms velocity profiles at six different axial positions for reacting flow of case S45-BB25P.

Figure 11 .
Figure 11.(a) Axial variation of pressure along the centreline for case S45-BB25P.(b) The gauge pressure field in the mid r-x plane for the non-reacting (left) and reacting flows (right) of case S45-BB25P.

Figure 14 .
Figure 14.(a) The mean axial velocity at the centreline for the reacting cases, (b) the characteristic lengths of the CRZ and (c) a schematic with the details of the characteristic lengths.

Figure 15 .
Figure15.The swirl number and blockage ratios investigated in this study.� is for cases in which the VBB and CRZ are separate, � is for cases in which the VBB and CRZ are merged in non-reacting, but separate in reacting flow and � is for the case in which the VBB and CRZ are merged in both nonreacting and reacting flow.

Table 1 .
Details of the cases studied.